Let kG be the group algebra of a finite group G over a field k of characteristic p, where p is a prime. Fix a non-trivial normal p-subgroup Q of G. In this paper, we study Auslander-Reiten sequences terminating at indecomposable kc-modules whose vertices are Q and whose sources are factor modules of kQ by some power of its radical. In particular, we consider relative projectivity of the middle terms of those sequences. In our main theorem, we shall prove that, for any subgroup H of G with Q < H < G, the middle term is H-projective if and only if the head of the third term is. We can also show that the head of the third term and some indecomposable direct summand of the middle term have vertices in common unless the former is Q-projective. In the case where Q is cyclic, these can be applied to all the AuslanderReiten sequences terminating at indecomposable kG-modules with vertices Q, since any such module has a source of the above form. The result in this case is related to a recent work of Erdmann [3] (see Section 3). The proof of the if part of the theorem is a direct consequence of [S, Theorem 5.41, whereas the only if part, whose proof is the main body of the present paper, can be proved by easy calculations. Notation is standard. For an indecomposable kG-module W, a vertex of W is denoted by ux( W). If a kG-module W’ is isomorphic to a direct summand of another kG-module IV”, we write IV’1 W”. Also Horn&W’, W”) is simply denoted by (IV’, W”) for convenience. J and J,, mean the Jacobson radicals of kG and kQ, respectively. Note that J,, is just the augmentation ideal of kQ. For any non-projective indecomposable kG-module W,